Theory

Once a fan designer has decided whether to use a lower (sleeve bearings) or a higher (anti-friction bearings) pair then the following results may be stated:

1) In a lower pair, the two surfaces conform to each other and contact will be dispersed over the whole of the nomi­nal area of contact. However, practical surfaces are never completely smooth and true contact will be restricted to a limited number of peaks. A rough rule is that the true area of contact will be only about 0.1% of the nominal area, whilst the total area of the peaks in contact equals the total load on the surfaces divided by the “flow stress” of the ma­terial.

2) In a higher pair, contact is within a narrow zone (usually an ellipse) in the vicinity of a point (ball bearings) or a line (roller bearings). Because of this concentration, stress is high and results in local elastic deformation. The actual area of contact is determined by the load, the geometrical shape of the contacting parts and the elasticity of the ma­terials involved. The mathematical determination of the contact conditions was first outlined by Hertz in 1886, such contacts thereafter being described as Hertzian and ac­cepted as “elastic”.

Bearing materials

It is obvious that the considerable differences between sleeve and ball/roller bearings will lead to completely different materi­als of construction being chosen.

In the case of sleeve bearings, the journal surface is usually made of a soft material which will conform readily to the harder shaft material. It is preferable to select materials which have a considerable difference in hardness so that the permanent shape of the bearing is determined by the harder surface.

Thus in a fan bearing, where a unidirectional load is transmitted from a rotating shaft to a stationary bearing housing, the shaft would be manufactured from an alloy steel, which would retain its shape, whilst the bearing housing would be lined with “white” metal or “babitt”, which would take up the shape of the shaft as shown in Figure 10.1.

In the past the bearing lining would be scraped by hand to con­form to the shaft. The author, in his apprenticeship days, spent many happy hours blueing, rolling and scraping! Now, however, it is usual to machine slightly oversize. Conformity is then achieved from a light “running-in”.

Assuming that the shaft is truly round, the surfaces will rapidly settle down to close conformity with negligible wear

Theory

Riff* Wrong

I a a d dиrrctlee fltcd ta tpact

Theory

Figure 10.1 Position of bearing lining relative to direction of load

For concentrated contacts, as in anti-friction (ball/roller) bear­ings, high values of Hertzian stress dictate that very hard mate­rials be used for all contacting surfaces. Either case-hardened or through-hardened steel is normally used.

Lubrication principles (hydrostatic and hydrodynamic)

The differences between sleeve and antifriction bearings are also most apparent when considering lubrication. When load and relative sliding velocity are low, lubrication requirements may be minimal and indeed unnecessary. The only problem is to dissipate the heat generated, there being no circulated lubricant to aid the process.

Where loads are substantial, oil, water or even gas may be forced between the surfaces at sufficient pressure to balance the external load, and to separate them. This is known as “hy­drostatic” lubrication.

When the closely conforming surfaces of a lower pair are slightly modified to produce a wedge-shaped gap filled with lu­bricant and when the surfaces are rotated, a pumping action will be generated within the bearing. This is called “hydrodynamic” lubrication.

Although it had obviously been used within bearings for many years it was not until Tower described some experiments con­ducted by him in 1885, that its existence was recognised. Some journal bearings used by the London Metropolitan Railway had a plug in a hole in the loaded crown. This was repeatedly ejected during his oil bath lubrication experiments. As a result he investigated the oil pressure distribution with the results shown in Figure 10.2. To preserve the historical flavour, the original Imperial units have been retained.

Reynolds’ equation

The theoretical basis for lubrication was derived by Reynolds in 1886. Despite its age, the equation continues to give accurate results, except at the extremes of the parameters detailed.

Thus:

(Ui + U2)| + 2V

Where:

P = pressure

On some large high speed fans, sleeve bearings may be the only viable bearing system as rolling element bearings have a short life and/or insufficient load carrying capacity. As a rough guide, a peripheral speed of about 8 m/s is required for an oil film and wedge to form for satisfactory operation. Below this speed sleeve bearings may not be viable.

Figure 10.2 Beauchamp Tower’s experimental results

подпись: 
figure 10.2 beauchamp tower’s experimental results
Atypical sleeve bearing will consist of a plain hard shaft journal and a soft metal sleeve which is often split on the horizontal centreline to aid assembly. Lubrication oil is fed into the sleeve area by means of rings running on the shaft and in grooves in the sleeve or by means of oil from an integral header tank, topped up by a disc system. In each case the oil is contained in a reservoir under the bearing and the rings or disc are immersed in the oil.

Often the exterior of the housing is provided with fins to help dis­sipate the heat which has been generated (see Figure 10.3).

Ut &

U2

подпись: ut &
u2
Theory= tangential velocity of the two surfaces

•n

H

подпись: •n
h
= velocity of approach = viscosity of the lubricant = distance between surfaces

X = measured in the direction of motion

Z = measured at right angles to the motion

For hydrodynamic action to be complete, the fluid film must be sufficiently thick to separate the shaft and bearing journal by an amount which exceeds the sum of the peaks on the two surfaces.

*rn

подпись: *rn TheoryThe thickness h of the lubricantfilm is therefore of critical impor­tance. In any particular case it is determined by the product of two factors — a hydrodynamic factor in which applied force is matched against the combined action of viscosity and velocity, and a geometrical factor dependent on the type of pad.

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